I need some ink for the Canon MX350.
However, the ink which came with my printer is Canon PG-510 (black).

Assuming that the PG-510 cartridge came with a new printer I suspect that it was fitted with what the trade calls "starter cartridges" which are partially-filled ones. Some (? most, ? all) new printers are supplied with these. My guess is that the PG-210 is the dinkum full one.